Adomian Decomposition, Firing Change Process Analysis and Synchronous Control of Fractional-Order Hindmarsh–Rose Neurons in Electromagnetic Field

Simulating fractional order systems using multistage Adomian decomposition method

Nonlinear phenomena play a crucial role in applied mathematics and physics. Analytic solutions of nonlinear equations are of fundamental importance and various methods for obtaining analytic solutions have been proposed. In this paper an application of the Adomian decomposition method is introduced for solving nonlinear fractional equations. The results reveal that the proposed method is very e...

Synchronous Firing and Its Influence on the Brain’s Electromagnetic Field

The human brain consists of approximately 100 billion electrically active neurones that generate an endogenous electromagnetic (em) field, whose role in neuronal computing has not been fully examined. The source, magnitude and likely influence of the brain’s endogenous em field are here considered. An estimate of the strength and magnitude of the brain’s em field is gained from theoretical cons...

Adaptive Fractional-order Control for Synchronization of Two Coupled Neurons in the External Electrical Stimulation

This paper addresses synchronizing two coupled chaotic FitzHugh–Nagumo (FHN) neurons with weakly gap junction under external electrical stimulation (EES). To transmit information among coupled neurons, by generalization of the integer-order FHN equations of the coupled system into the fractional-order in frequency domain using Crone approach, the behavior of each coupled neuron relies on its pa...

Dynamics of the Fractional-order Lorenz System Based on Adomian Decomposition Method and Its DSP Implementation

Dynamics and digital circuit implementation of the fractional-order Lorenz system are investigated by employing Adomian decomposition method (ADM). Dynamics of the fractional-order Lorenz system with derivative order and parameter varying is analyzed by means of Lyapunov exponents (LEs), bifurcation diagram, chaos diagram and phase diagram. Results show that the fractional-order Lorenz system h...

Synchronous Firing and Its Influence on the Brain’s Electromagnetic Field: Evidence for an Electromagnetic Field Theory of Consciousness